# Intermediately trimmed strong laws for Birkhoff sums on subshifts of finite type

## TL;DR

This paper establishes strong laws of large numbers with intermediate trimming for Birkhoff sums on subshifts of finite type, extending previous results and introducing new function spaces.

## Contribution

It introduces intermediate trimming laws for Birkhoff sums on subshifts of finite type and develops the space of quasi-Hölder functions for these systems.

## Key findings

- Proves strong laws of large numbers with intermediate trimming.
- Provides examples of St. Petersburg type distributions for Markov measures.
- Extends trimming results from interval maps to subshifts of finite type.

## Abstract

We prove strong laws of large numbers under intermediate trimming for Birkhoff sums over subshifts of finite type. This gives another application of a previous trimming result only proven for interval maps. In case of Markov measures we give a further example of St.\ Petersburg type distribution functions. To prove these statements we introduce the space of quasi-H\"older continuous functions for subshifts of finite type.